Compressed Sensing in Magnetic Resonance Imaging Using the Multi-step Fresnel Domain Band Split Transformation

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Purpose: We present and demonstrate a new compressed sensing (CS) method to improve the image quality obtained in magnetic resonance CS. The sparsifying function, which transforms the image function to sparsified domain, is very important since it controls the quality of reconstructed image. We investigate the utility of a multi-step directional transform for improving the quality of reconstructed images in CS reconstruction. Methods: As a sparsifying function, we used the Fresnel domain band split transformation (FREBAS), a method to decompose images with highly directional representation and optional scaling of the decomposition. Our image reconstruction algorithm involved linear and nonlinear operations, such as projection onto a convex set and hard thresholding in the transform domain. Results: Several numerical experiments demonstrated the acquisition of images of better quality using multi-step successive thresholding and different scaling parameters in the FREBAS domain rather than single-step FREBAS thresholding. Reconstruction experiments showed much more detail of the imaging subject with fewer artifacts in CS images based on the FREBAS transform compared to CS based on the wavelet transform. Conclusion: The proposed method using multi-step FREBAS as the sparsifying transformation function is suitable for CS magnetic resonance imaging.